1. TAMR+ Defined: Temporal-Adaptive Multi-hop Reasoning
TAMR+ is a knowledge graph reasoning methodology developed by Harish Kumar at Quantamix Solutions B.V. and published in SSRN working paper 6359818. It was designed specifically to address the failure modes of standard large language model retrieval architectures when applied to structured regulatory domains.
The name encodes the three core innovations that differentiate TAMR+ from prior graph reasoning approaches:
Every regulatory node in the knowledge graph carries temporal validity metadata: date entered into force, date applicable, and date superseded. TAMR+ filters nodes by temporal validity at query time — it cannot retrieve a regulatory requirement that is not yet applicable or has been superseded. Standard graph RAG approaches lack this temporal layer and hallucinate superseded article versions.
TAMR+ dynamically adjusts its reasoning strategy based on query classification. Obligation queries (what must we do?) use a depth-first traversal that prioritizes direct obligation nodes. Penalty queries use a breadth-first approach that collects all applicable penalty provisions. Classification queries use a decision-tree traversal through risk classification nodes. This adaptive routing eliminates the noise inherent in uniform retrieval strategies.
EU AI Act obligations are rarely self-contained in a single article. Article 9 (risk management) is prerequisite for Article 43 (conformity assessment). Article 13 (transparency) generates obligations for both Article 28 (deployer) and Article 53 (GPAI provider). TAMR+ follows these dependency edges across multiple hops — up to seven in the most complex obligation chains — producing answers that reflect the full legal context.
2. Why Vector Search Fails for Regulatory Compliance: Fragmented Context and Hallucinated Citations
Vector search — the retrieval backbone of most commercial RAG systems — converts text into high-dimensional embeddings and finds chunks with the highest cosine similarity to the query embedding. For many knowledge domains, this works adequately. For regulatory compliance, it fails systematically, in five recurring ways.
The Five Failure Modes
Article fragmentation
EU AI Act articles are split into recitals, paragraphs, and sub-paragraphs when chunked for embedding. Obligation chains that span multiple paragraphs (e.g., Article 9(1) through 9(8)) are retrieved as disconnected fragments. The assembling LLM then synthesizes an answer from incomplete context, producing plausible but legally inaccurate responses.
Cross-reference blindness
EU regulatory texts use extensive cross-referencing. 'As referred to in Article 6(2)' and 'in accordance with Annex III' are precise legal pointers. Vector search cannot follow these references — it retrieves the chunk containing the reference but not the target. Multi-hop reasoning resolves this by traversing reference edges in the graph.
Temporal staleness
EU AI Act has a staggered applicability timeline: February 2025 (prohibitions), August 2025 (GPAI), August 2026 (Article 50), December 2027 (Annex III), August 2028 (Annex I). Vector embeddings do not encode this temporal structure. Asking 'what are my obligations today?' to a vector system returns all articles regardless of whether they are yet applicable.
Exception logic failures
Regulatory exceptions modify or override general obligations. Article 53(2) creates an open-source GPAI exemption that modifies the general Article 53 obligations. Vector search retrieves both the general obligation and the exception as separate chunks; the LLM frequently fails to correctly apply the exception to the general rule when synthesizing its answer.
Citation hallucination
When retrieved chunks do not contain a sufficient answer, LLMs fill the gap by generating plausible-sounding article numbers. Vector-based systems can produce hallucinated citations (article numbers that do not exist or do not say what the model claims). TAMR+ is designed to cite only nodes that exist in its knowledge graph.
3. Graph Representation: EU AI Act as a Knowledge Graph with 31 OWL Entity Types and Temporal Edges
TAMR+ represents the EU AI Act (and other regulations) as an OWL (Web Ontology Language) knowledge graph. This representation captures the legal structure of the regulation, not merely its text.
The graph is organised around 31 entity types. Key entity types include AISystem, HighRiskAISystem, GPAIModel, SystemicRiskGPAI, Provider, Deployer, Obligation, ProhibitedPractice, Exception, Threshold, ConformityAssessmentProcedure, Annex, ImplementingAct, DelegatedAct, and HarmonisedStandard. Each entity type has defined properties and relationship types with formal OWL semantics — enabling logical inference rather than just graph traversal.
Temporal Edges
Every obligation node carries four temporal edge types: IN_FORCE_FROM (regulatory entry into force date), APPLICABLE_FROM (date organizations must comply), SUPERSEDED_BY (if replaced by a later provision), and MODIFIED_BY (if an implementing act changes the obligation). At query time, TAMR+ accepts a reference date and filters the graph to return only nodes whose APPLICABLE_FROM is before the reference date and whose SUPERSEDED_BY edge either does not exist or points to a node with a future APPLICABLE_FROM.
Practical impact: On 1 December 2027 — one day before the Annex III high-risk AI provisions become applicable — a TAMR+ query about high-risk AI obligations correctly returns zero applicable high-risk obligations. On 2 December 2027, the same query returns all Article 9–17 obligations. Vector-based systems cannot make this distinction and generate incorrect answers in both cases.
4. Multi-Hop Reasoning: How the Algorithm Traverses Regulatory Article Dependencies
The most legally sophisticated regulatory questions require the system to traverse several dependency edges to produce a correct answer. An example: “Does a European SME providing a high-risk AI system for medical diagnosis need to undergo a third-party conformity assessment?”
Answering this correctly requires the system to: (1) classify the system as high-risk under Annex III (medical diagnosis); (2) determine whether Article 43 requires third-party assessment for this category (yes, for medical devices); (3) check whether the SME exception in Article 55 applies (it does not for third-party assessment requirements in medical); (4) identify which conformity assessment procedure is applicable; and (5) note that Article 10 data quality obligations must be met before conformity assessment can begin.
TAMR+ handles this through a directed graph traversal that follows REQUIRES, QUALIFIES, OVERRIDES, and REFERENCES edge types. The traversal algorithm maintains a reasoning trace that records every node visited and every edge followed — producing not just the answer but the full reasoning path with article citations, which is essential for regulatory audit documentation.
5. Adaptive Weighting: Temporal Relevance Scoring for Recently Amended Articles
The EU AI Act is a living document. The EU AI Office has issued implementing acts, the GPAI Code of Practice has been finalized, and harmonised standards under Article 40 are progressively being published. TAMR+'s adaptive weighting system assigns a temporal relevance score to each knowledge graph node, which modulates retrieval priority.
| Signal | Weight Modifier | Rationale |
|---|---|---|
| Published < 90 days ago | +0.3 | Recently amended provisions have highest compliance relevance |
| Supersedes earlier provision | +0.2 | Superseding node is the current authoritative text |
| Referenced by harmonised standard | +0.15 | Presumption of conformity elevates operational relevance |
| Under consultation / pending | -0.2 | Reduce retrieval priority for non-final provisions |
| Not yet applicable | -0.4 | Pre-applicability nodes are lower priority but visible for planning |
6. Evaluation Status
Benchmark figures for TAMR+ are not published until their source files are released (doi.org/10.5281/zenodo.18929634). This article therefore reports no benchmark result for TAMR+.
Answers are scored with TRACE, a five-dimension score between 0 and 1. It is not an accuracy rate. A new evaluation run with a real vector-only comparison, gold-answer scoring and retained artefacts is planned; until it is published, the comparison with vector search in this article is an argument from architecture, not a measured result.
7. Cost at Retrieval Time
TAMR+ makes no LLM calls during retrieval: the graph traversal is deterministic, so the model is called only to write the answer. Retrieval methods that index or navigate documents with an LLM add model calls before the answer is written. Benchmark figures for TAMR+, including cost and latency comparisons, are not published until their source files are released.
8. Patent Application EP26162901.8 (Pending)
European patent application EP26162901.8 was filed by Quantamix Solutions B.V. under the European Patent Convention and is pending. A pending application confers no granted rights. The application is directed to three areas:
OWL Regulatory Knowledge Graph with Temporal Validity Edges
The specific method of constructing legal knowledge graphs using OWL ontologies with temporal validity edge types (IN_FORCE_FROM, APPLICABLE_FROM, SUPERSEDED_BY, MODIFIED_BY) and the query-time temporal filtering algorithm that uses these edges to return only currently applicable provisions.
Adaptive Multi-hop Traversal with Query-Type Classification
The method of classifying incoming regulatory queries into obligation, penalty, classification, and timeline types, and dynamically selecting traversal strategies (depth-first, breadth-first, decision-tree) based on query type to optimize both accuracy and computational efficiency.
Temporal Relevance Subgraph Caching with Regulatory Update Invalidation
The caching architecture that pre-computes frequent regulatory reasoning paths as cached subgraphs, assigns temporal relevance scores to determine cache priority, and implements regulatory update detection with automatic cache invalidation for affected subgraphs within a defined propagation time.
The scope of any patent will depend on the claims as finally granted. GraQle, the commercial implementation, licenses TAMR+ under its enterprise tier.
9. FAQ
What does TAMR+ stand for?
TAMR+ stands for Temporal-Adaptive Multi-hop Reasoning. Temporal reflects the algorithm's ability to weight regulatory articles by recency and applicability date. Adaptive means reasoning paths are dynamically adjusted based on query type. Multi-hop means the algorithm traverses multiple dependency edges. The '+' suffix denotes the enhanced version with subgraph caching and cross-framework reasoning, which are the basis of patent application EP26162901.8 (pending).
Why does vector search fail for regulatory compliance questions?
Vector search fails because regulatory obligations are distributed across multiple cross-referenced articles (lost when chunked), temporal applicability cannot be represented in static embeddings, exception logic requires graph traversal to evaluate correctly, and LLMs hallucinate article citations when retrieved context is insufficient..
What does the TAMR+ paper report on evaluation?
Benchmark figures for TAMR+ are not published until their source files are released. Until a new evaluation run with retained artefacts is published, no benchmark result for TAMR+ is reported here (doi.org/10.5281/zenodo.18929634).
What does patent application EP26162901.8 (pending) cover?
Patent application EP26162901.8 is pending at the European Patent Office. It was filed by Quantamix Solutions B.V. and covers the methods described in the TAMR+ paper, including knowledge-graph-based multi-signal retrieval and the TRACE scoring and gap attribution method. A pending application confers no granted rights; the scope of any patent depends on the claims as finally granted.
How does TAMR+ handle regulatory amendments and updates?
TAMR+ handles regulatory amendments through temporal edge management. Each node carries dateInForce, dateApplicable, and dateSuperseded properties. When regulatory updates are detected, affected nodes are updated and their temporal properties modified. Queries cannot retrieve nodes that the temporal filter marks as inactive for the query date.
Related guides
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